The introduction of time-fractional derivatives in the Navier-Stokes equations goes back to Lions and was recently extensively studied by many authors. When motivating such problems authors tend generally to motivate fractional models instead. In some papers (the ones of Zhou and Peng for example) say that such equations can model anomalous diffusion in fractal media. What I am looking for is some concrete situations where time-fractional Navier-Stokes equations is the good way to model the fluid flow.
Dear Akhlil Khalid
There are many types of differentiation such as , Material derivative , Partial derevative ,Analytical derevative , Time fractional derevative .
And Navier-Stokes equations use almost all types .
Please kindly consult this article :
https://www.sciencedirect.com/science/article/pii/S2090447917300229?via%3Dihub
In order to get an answer to your question .
A number of papers handle this problem, for example, see
http://emis.math.tifr.res.in/journals/GMN/yahoo_site_admin/assets/docs/5_GMN-342-V4N2.160165230.pdf
Existence and approximations of solutions for time-fractional Navier-stokes equations
Peng, Li, Debbouche, Amar, Zhou, YongJournal:Mathematical Methods in the Applied SciencesYear:2018
An analysis and comparison of the time accuracy of fractional-step methods for the Navier–Stokes equations on staggered grids
S. Armfield, R. StreetJournal:International Journal for Numerical Methods in FluidsYear:2002
Thank you all for the answers and the suggestions. It will be certainly helpful for my research.
- Badges
- Science topic
- Similar topics
- Engineering
- Thermal Engineering
- Thermofluid
- Fluid Mechanics
- Fluid Dynamics